两类16p阶群的三度正规Cayley图的比较  

Comparison of Three Degree Normal Cayley Graphs of Two Classes of 16p Order Groups

作　　者：董留栓[1] Dong Liu Shuan(College of Information and Business,Zhongyuan University of Technology,Zhengzhou 450007,China)

机构地区：[1]中原工学院信息商务学院,郑州450002

出　　处：《黑龙江科学》2020年第10期20-21,共2页Heilongjiang Science

摘　　要：有限群G的一个Cayley图X=Cay(G,S)称为正规的,如果右乘变换群R(G)在Aut(G)中正规。本研究对16p阶群G1=〈a,b|a^8p=b^2=1,a^b=a^4p+1〉和群G2=〈a,b|a^8p=b^2=1,a^b=a^4p-1〉的3度Cayley图作比较,其中p为奇素数,得到两者均有一个图是正规Cayley图且同构、且A1≌Z2的结论。A Cayley graph X=Cay(G,S)of a finite group G is defined as normal,if R(G),the group of right multiplications,is normal in Aut X.In this paper,by investigating the nomality,we compare 3-valent connected Cayley graphs of groups of order 16 p of G1=〈a,b|a^8p=b^2=1,a^b=a^4p+1〉to 3-valent connected Cayley graphs of G2=〈a,b|a^8p=b^2=1,a^b=a^4p-1〉where p is odd prime.we obtain that they are isomorphic graphs.

关 键 词：CAYLEY图 正规CAYLEY图 16p阶群 

分 类 号：O157.5[理学—数学] O152.1[理学—基础数学]